Construct Single-Hierarchical P/NBD Model for CD-Now Transaction Data
In this workbook we construct the non-hierarchical P/NBD models on the synthetic data with the longer timeframe.
1 Load and Construct Datasets
1.1 Load CD-NOW Transaction Data
We now want to load the CD-NOW transaction data.
Show code
customer_cohortdata_tbl <- read_rds("data/cdnow_customer_cohort_data_tbl.rds")
customer_cohortdata_tbl |> glimpse()Rows: 23,570
Columns: 5
$ customer_id <chr> "00001", "00002", "00003", "00004", "00005", "00006", …
$ cohort_qtr <chr> "1997 Q1", "1997 Q1", "1997 Q1", "1997 Q1", "1997 Q1",…
$ cohort_ym <chr> "1997 01", "1997 01", "1997 01", "1997 01", "1997 01",…
$ first_tnx_date <date> 1997-01-01, 1997-01-12, 1997-01-02, 1997-01-01, 1997-…
$ total_tnx_count <int> 1, 2, 6, 4, 11, 1, 3, 8, 3, 1, 4, 1, 1, 1, 1, 4, 1, 1,…
Show code
customer_transactions_tbl <- read_rds("data/cdnow_transaction_data_tbl.rds")
customer_transactions_tbl |> glimpse()Rows: 69,659
Columns: 8
$ customer_id <chr> "00001", "00002", "00002", "00003", "00003", "00003", "0…
$ tnx_date <date> 1997-01-01, 1997-01-12, 1997-01-12, 1997-01-02, 1997-03…
$ tnx_timestamp <dttm> 1997-01-01 21:57:19, 1997-01-12 06:52:02, 1997-01-12 22…
$ tnx_dow <fct> Wed, Sun, Sun, Thu, Sun, Wed, Sat, Tue, Thu, Wed, Sat, S…
$ tnx_month <fct> Jan, Jan, Jan, Jan, Mar, Apr, Nov, Nov, May, Jan, Jan, A…
$ tnx_week <chr> "00", "01", "01", "00", "12", "13", "45", "47", "21", "0…
$ cd_count <int> 1, 5, 1, 2, 2, 2, 5, 4, 1, 2, 2, 1, 2, 2, 1, 3, 3, 3, 2,…
$ total_spend <dbl> 11.77, 77.00, 12.00, 20.76, 20.76, 19.54, 57.45, 20.96, …
Show code
customer_subset_id <- read_rds("data/cdnow_customer_subset_ids.rds")
customer_subset_id |> glimpse() chr [1:2000] "00014" "00018" "00032" "00061" "00064" "00076" "00081" ...
We re-produce the visualisation of the transaction times we used in previous workbooks.
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plot_tbl <- customer_transactions_tbl |>
group_nest(customer_id, .key = "cust_data") |>
filter(map_int(cust_data, nrow) > 3) |>
slice_sample(n = 30) |>
unnest(cust_data)
ggplot(plot_tbl, aes(x = tnx_timestamp, y = customer_id)) +
geom_line() +
geom_point() +
labs(
x = "Date",
y = "Customer ID",
title = "Visualisation of Customer Transaction Times"
) +
theme(axis.text.y = element_text(size = 10))1.2 Load Derived Data
Show code
obs_fitdata_tbl <- read_rds("data/cdnow_obs_fitdata_tbl.rds")
obs_validdata_tbl <- read_rds("data/cdnow_obs_validdata_tbl.rds")
customer_fit_stats_tbl <- obs_fitdata_tbl |>
rename(x = tnx_count)1.3 Load Subset Data
We also want to construct our data subsets for the purposes of speeding up our valuations.
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customer_fit_subset_tbl <- obs_fitdata_tbl |>
filter(customer_id %in% customer_subset_id)
customer_fit_subset_tbl |> glimpse()Rows: 2,000
Columns: 6
$ customer_id <chr> "00014", "00018", "00032", "00061", "00064", "00076", "…
$ first_tnx_date <dttm> 1997-01-01 21:18:22, 1997-01-04 18:49:57, 1997-01-01 1…
$ last_tnx_date <dttm> 1997-01-01 21:18:22, 1997-01-04 18:49:57, 1997-01-24 1…
$ tnx_count <dbl> 0, 0, 1, 0, 8, 0, 13, 12, 0, 2, 0, 6, 0, 0, 1, 1, 0, 0,…
$ t_x <dbl> 0.0000000, 0.0000000, 3.3184159, 0.0000000, 51.5902377,…
$ T_cal <dbl> 52.01604, 51.60219, 52.06928, 52.11594, 51.82785, 52.12…
Show code
customer_valid_subset_tbl <- obs_validdata_tbl |>
filter(customer_id %in% customer_subset_id)
customer_valid_subset_tbl |> glimpse()Rows: 2,000
Columns: 3
$ customer_id <chr> "00014", "00018", "00032", "00061", "00064", "00076"…
$ tnx_count <dbl> 0, 0, 1, 0, 4, 0, 0, 6, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0…
$ tnx_last_interval <dbl> NA, NA, 9.945594, NA, 25.052557, NA, NA, 25.303557, …
We now use these datasets to set the start and end dates for our various validation methods.
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dates_lst <- read_rds("data/cdnow_simulation_dates.rds")
use_fit_start_date <- dates_lst$use_fit_start_date
use_fit_end_date <- dates_lst$use_fit_end_date
use_valid_start_date <- dates_lst$use_valid_start_date
use_valid_end_date <- dates_lst$use_valid_end_dateBefore we start on that, we set a few parameters for the workbook to organise our Stan code.
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stan_modeldir <- "stan_models"
stan_codedir <- "stan_code"2 Fit First Hierarchical Lambda Model
Our first hierarchical model puts a hierarchical prior around the mean of our population \(\lambda\) - lambda_mn.
Once again we use a Gamma prior for it.
2.1 Compile and Fit Stan Model
We now compile this model using CmdStanR.
Show code
pnbd_onehierlambda_stanmodel <- cmdstan_model(
"stan_code/pnbd_onehier_lambda.stan",
include_paths = stan_codedir,
pedantic = TRUE,
dir = stan_modeldir
)We then use this compiled model with our data to produce a fit of the data.
Show code
stan_modelname <- "pnbd_cdnow_onehierlambda1"
stanfit_prefix <- str_c("fit_", stan_modelname)
stanfit_seed <- stanfit_seed + 1
stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")
stan_data_lst <- customer_fit_stats_tbl |>
select(customer_id, x, t_x, T_cal) |>
compose_data(
hier_lambda_mn_p1 = 0.25,
hier_lambda_mn_p2 = 1,
lambda_cv = 1.00,
mu_mn = 0.10,
mu_cv = 1.00,
)
if(!file_exists(stanfit_object_file)) {
pnbd_cdnow_onehierlambda1_stanfit <- pnbd_onehierlambda_stanmodel$sample(
data = stan_data_lst,
chains = 4,
iter_warmup = 500,
iter_sampling = 500,
seed = stanfit_seed,
save_warmup = TRUE,
output_dir = stan_modeldir,
output_basename = stanfit_prefix,
)
pnbd_cdnow_onehierlambda1_stanfit$save_object(stanfit_object_file, compress = "gzip")
} else {
pnbd_cdnow_onehierlambda1_stanfit <- read_rds(stanfit_object_file)
}
pnbd_cdnow_onehierlambda1_stanfit$summary()# A tibble: 70,713 × 10
variable mean median sd mad q5 q95 rhat ess_bulk
<chr> <num> <num> <num> <num> <num> <num> <num> <num>
1 lp__ -2.47e+5 -2.47e+5 1.70e+2 1.65e+2 -2.48e+5 -2.47e+5 1.00 604.
2 lambda_mn 6.59e-2 6.59e-2 6.75e-4 6.93e-4 6.48e-2 6.71e-2 1.00 1276.
3 lambda[1] 4.66e-2 2.94e-2 5.19e-2 3.22e-2 1.86e-3 1.48e-1 1.00 2527.
4 lambda[2] 1.00e-1 8.08e-2 7.73e-2 6.14e-2 1.46e-2 2.50e-1 1.00 2858.
5 lambda[3] 7.60e-2 7.10e-2 3.43e-2 3.24e-2 2.94e-2 1.42e-1 1.00 2714.
6 lambda[4] 5.92e-2 5.42e-2 2.96e-2 2.73e-2 2.04e-2 1.15e-1 1.00 3443.
7 lambda[5] 1.49e-1 1.44e-1 4.60e-2 4.42e-2 8.05e-2 2.32e-1 1.00 2651.
8 lambda[6] 4.72e-2 2.86e-2 5.15e-2 3.16e-2 1.96e-3 1.56e-1 1.00 2457.
9 lambda[7] 3.12e-2 2.62e-2 2.17e-2 1.88e-2 5.72e-3 7.48e-2 0.999 2306.
10 lambda[8] 1.05e-1 1.01e-1 3.85e-2 3.64e-2 5.19e-2 1.77e-1 1.01 3286.
# ℹ 70,703 more rows
# ℹ 1 more variable: ess_tail <num>
We have some basic HMC-based validity statistics we can check.
Show code
pnbd_cdnow_onehierlambda1_stanfit$cmdstan_diagnose()File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda1-1.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda1-2.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda1-3.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda1-4.csv not found
No valid input files, exiting.
2.2 Visual Diagnostics of the Sample Validity
Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.
Show code
parameter_subset <- c(
"lambda_mn",
"lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
"mu[1]", "mu[2]", "mu[3]", "mu[4]"
)
pnbd_cdnow_onehierlambda1_stanfit$draws(inc_warmup = FALSE) |>
mcmc_trace(pars = parameter_subset) +
expand_limits(y = 0) +
labs(
x = "Iteration",
y = "Value",
title = "Traceplot of Sample of Lambda and Mu Values"
) +
theme(axis.text.x = element_text(size = 10))We also check \(N_{eff}\) as a quick diagnostic of the fit.
Show code
pnbd_cdnow_onehierlambda1_stanfit |>
neff_ratio(pars = c("lambda", "mu")) |>
as.numeric() |>
mcmc_neff() +
ggtitle("Plot of Parameter Effective Sample Sizes")2.3 Assess the Model
As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.
Show code
pnbd_stanfit <- pnbd_cdnow_onehierlambda1_stanfit |>
recover_types(customer_fit_stats_tbl)
pnbd_cdnow_onehierlambda1_assess_data_lst <- run_model_assessment(
model_stanfit = pnbd_stanfit,
insample_tbl = customer_fit_subset_tbl,
fit_label = "pnbd_cdnow_onehierlambda1",
fit_end_dttm = use_fit_end_date |> as.POSIXct(),
valid_start_dttm = use_valid_start_date |> as.POSIXct(),
valid_end_dttm = use_valid_end_date |> as.POSIXct(),
sim_seed = 4210
)
pnbd_cdnow_onehierlambda1_assess_data_lst |> glimpse()List of 5
$ model_fit_index_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda1_assess_fit_index_tbl.rds"
$ model_valid_index_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda1_assess_valid_index_tbl.rds"
$ model_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda1_assess_model_simstats_tbl.rds"
$ model_fit_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda1_assess_fit_simstats_tbl.rds"
$ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_onehierlambda1_assess_valid_simstats_tbl.rds"
2.3.1 Check In-Sample Data Validation
We first check the model against the in-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehierlambda1_assess_data_lst |>
use_series(model_fit_simstats_filepath) |>
read_rds()
insample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = obs_fitdata_tbl,
simdata_tbl = simdata_tbl
)
insample_plots_lst$multi_plot |> print()Show code
insample_plots_lst$total_plot |> print()Show code
insample_plots_lst$quant_plot |> print()This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.
2.3.2 Check Out-of-Sample Data Validation
We now repeat for the out-of-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehierlambda1_assess_data_lst |>
use_series(model_valid_simstats_filepath) |>
read_rds()
outsample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = obs_validdata_tbl,
simdata_tbl = simdata_tbl
)
outsample_plots_lst$multi_plot |> print()Show code
outsample_plots_lst$total_plot |> print()Show code
outsample_plots_lst$quant_plot |> print()As for our short time frame data, overall our model is working well.
3 Fit Second Hierarchical Lambda Model
In this model, we are going with a broadly similar model but we are instead using a different mean for our hierarchical prior.
3.1 Fit Stan Model
We now want to fit the model to our data using this alternative prior for lambda_mn.
Show code
stan_modelname <- "pnbd_cdnow_onehierlambda2"
stanfit_prefix <- str_c("fit_", stan_modelname)
stanfit_seed <- stanfit_seed + 1
stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")
stan_data_lst <- customer_fit_stats_tbl |>
select(customer_id, x, t_x, T_cal) |>
compose_data(
hier_lambda_mn_p1 = 0.50,
hier_lambda_mn_p2 = 1,
lambda_cv = 1.00,
mu_mn = 0.10,
mu_cv = 1.00,
)
if(!file_exists(stanfit_object_file)) {
pnbd_cdnow_onehierlambda2_stanfit <- pnbd_onehierlambda_stanmodel$sample(
data = stan_data_lst,
chains = 4,
iter_warmup = 500,
iter_sampling = 500,
seed = stanfit_seed,
save_warmup = TRUE,
output_dir = stan_modeldir,
output_basename = stanfit_prefix,
)
pnbd_cdnow_onehierlambda2_stanfit$save_object(stanfit_object_file, compress = "gzip")
} else {
pnbd_cdnow_onehierlambda2_stanfit <- read_rds(stanfit_object_file)
}
pnbd_cdnow_onehierlambda2_stanfit$summary()# A tibble: 70,713 × 10
variable mean median sd mad q5 q95 rhat ess_bulk
<chr> <num> <num> <num> <num> <num> <num> <num> <num>
1 lp__ -2.47e+5 -2.47e+5 1.75e+2 1.76e+2 -2.48e+5 -2.47e+5 1.00 632.
2 lambda_mn 6.59e-2 6.59e-2 6.82e-4 7.20e-4 6.48e-2 6.70e-2 1.00 1451.
3 lambda[1] 4.71e-2 3.09e-2 4.98e-2 3.37e-2 2.38e-3 1.46e-1 1.00 2207.
4 lambda[2] 1.04e-1 8.46e-2 8.07e-2 6.38e-2 1.60e-2 2.61e-1 1.01 3083.
5 lambda[3] 7.60e-2 7.26e-2 3.26e-2 3.20e-2 3.16e-2 1.36e-1 1.00 2698.
6 lambda[4] 5.98e-2 5.56e-2 2.82e-2 2.77e-2 2.15e-2 1.12e-1 1.00 2937.
7 lambda[5] 1.48e-1 1.44e-1 4.62e-2 4.69e-2 8.07e-2 2.31e-1 1.00 4258.
8 lambda[6] 4.49e-2 2.96e-2 4.79e-2 3.04e-2 2.14e-3 1.38e-1 1.00 1991.
9 lambda[7] 3.04e-2 2.59e-2 2.12e-2 1.81e-2 4.85e-3 7.23e-2 1.00 2916.
10 lambda[8] 1.04e-1 9.86e-2 4.01e-2 3.78e-2 4.85e-2 1.78e-1 1.01 3718.
# ℹ 70,703 more rows
# ℹ 1 more variable: ess_tail <num>
We have some basic HMC-based validity statistics we can check.
Show code
pnbd_cdnow_onehierlambda2_stanfit$cmdstan_diagnose()File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda2-1.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda2-2.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda2-3.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehierlambda2-4.csv not found
No valid input files, exiting.
3.2 Visual Diagnostics of the Sample Validity
Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.
Show code
parameter_subset <- c(
"lambda_mn",
"lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
"mu[1]", "mu[2]", "mu[3]", "mu[4]"
)
pnbd_cdnow_onehierlambda2_stanfit$draws(inc_warmup = FALSE) |>
mcmc_trace(pars = parameter_subset) +
expand_limits(y = 0) +
labs(
x = "Iteration",
y = "Value",
title = "Traceplot of Sample of Lambda and Mu Values"
) +
theme(axis.text.x = element_text(size = 10))We also check \(N_{eff}\) as a quick diagnostic of the fit.
Show code
pnbd_cdnow_onehierlambda2_stanfit |>
neff_ratio(pars = c("lambda", "mu")) |>
as.numeric() |>
mcmc_neff() +
ggtitle("Plot of Parameter Effective Sample Sizes")3.3 Assess the Model
As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.
Show code
pnbd_stanfit <- pnbd_cdnow_onehierlambda2_stanfit |>
recover_types(customer_fit_stats_tbl)
pnbd_cdnow_onehierlambda2_assess_data_lst <- run_model_assessment(
model_stanfit = pnbd_stanfit,
insample_tbl = customer_fit_subset_tbl,
fit_label = "pnbd_cdnow_onehierlambda2",
fit_end_dttm = use_fit_end_date |> as.POSIXct(),
valid_start_dttm = use_valid_start_date |> as.POSIXct(),
valid_end_dttm = use_valid_end_date |> as.POSIXct(),
sim_seed = 4210
)
pnbd_cdnow_onehierlambda2_assess_data_lst |> glimpse()List of 5
$ model_fit_index_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda2_assess_fit_index_tbl.rds"
$ model_valid_index_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda2_assess_valid_index_tbl.rds"
$ model_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda2_assess_model_simstats_tbl.rds"
$ model_fit_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehierlambda2_assess_fit_simstats_tbl.rds"
$ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_onehierlambda2_assess_valid_simstats_tbl.rds"
3.3.1 Check In-Sample Data Validation
We first check the model against the in-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehierlambda2_assess_data_lst |>
use_series(model_fit_simstats_filepath) |>
read_rds()
insample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = customer_fit_subset_tbl,
simdata_tbl = simdata_tbl
)
insample_plots_lst$multi_plot |> print()Show code
insample_plots_lst$total_plot |> print()Show code
insample_plots_lst$quant_plot |> print()This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.
3.3.2 Check Out-of-Sample Data Validation
We now repeat for the out-of-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehierlambda1_assess_data_lst |>
use_series(model_valid_simstats_filepath) |>
read_rds()
outsample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = customer_valid_subset_tbl,
simdata_tbl = simdata_tbl
)
outsample_plots_lst$multi_plot |> print()Show code
outsample_plots_lst$total_plot |> print()Show code
outsample_plots_lst$quant_plot |> print()As for our short time frame data, overall our model is working well.
4 Fit First Hierarchical Mu Model
We now construct the same hierarchical model but based around mu_mn.
4.1 Compile and Fit Stan Model
We compile this model using CmdStanR.
Show code
pnbd_onehiermu_stanmodel <- cmdstan_model(
"stan_code/pnbd_onehier_mu.stan",
include_paths = stan_codedir,
pedantic = TRUE,
dir = stan_modeldir
)We then use this compiled model with our data to produce a fit of the data.
Show code
stan_modelname <- "pnbd_cdnow_onehiermu1"
stanfit_prefix <- str_c("fit_", stan_modelname)
stanfit_seed <- stanfit_seed + 1
stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")
stan_data_lst <- customer_fit_stats_tbl |>
select(customer_id, x, t_x, T_cal) |>
compose_data(
hier_mu_mn_p1 = 0.50,
hier_mu_mn_p2 = 1.00,
lambda_mn = 0.25,
lambda_cv = 1.00,
mu_cv = 1.00
)
if(!file_exists(stanfit_object_file)) {
pnbd_cdnow_onehiermu1_stanfit <- pnbd_onehiermu_stanmodel$sample(
data = stan_data_lst,
chains = 4,
iter_warmup = 500,
iter_sampling = 500,
seed = stanfit_seed,
save_warmup = TRUE,
output_dir = stan_modeldir,
output_basename = stanfit_prefix,
)
pnbd_cdnow_onehiermu1_stanfit$save_object(stanfit_object_file, compress = "gzip")
} else {
pnbd_cdnow_onehiermu1_stanfit <- read_rds(stanfit_object_file)
}
pnbd_cdnow_onehiermu1_stanfit$summary()# A tibble: 70,713 × 10
variable mean median sd mad q5 q95 rhat ess_bulk
<chr> <num> <num> <num> <num> <num> <num> <num> <num>
1 lp__ -2.33e+5 -2.33e+5 1.76e+2 1.73e+2 -2.33e+5 -2.32e+5 1.01 596.
2 mu_mn 1.15e-1 1.15e-1 1.84e-3 1.88e-3 1.12e-1 1.18e-1 1.00 674.
3 lambda[1] 1.40e-1 8.42e-2 1.61e-1 9.35e-2 4.72e-3 4.44e-1 1.00 2112.
4 lambda[2] 3.42e-1 2.66e-1 2.73e-1 2.24e-1 5.21e-2 8.82e-1 1.00 2637.
5 lambda[3] 9.00e-2 8.44e-2 3.87e-2 3.81e-2 3.73e-2 1.63e-1 1.00 3286.
6 lambda[4] 7.13e-2 6.68e-2 3.39e-2 3.21e-2 2.57e-2 1.35e-1 1.00 3082.
7 lambda[5] 1.78e-1 1.72e-1 5.64e-2 5.32e-2 9.77e-2 2.83e-1 1.00 3227.
8 lambda[6] 1.44e-1 8.89e-2 1.64e-1 1.01e-1 5.74e-3 4.72e-1 1.00 2337.
9 lambda[7] 3.77e-2 3.23e-2 2.65e-2 2.40e-2 6.59e-3 8.83e-2 1.01 3541.
10 lambda[8] 1.24e-1 1.17e-1 4.80e-2 4.62e-2 5.63e-2 2.13e-1 1.00 4494.
# ℹ 70,703 more rows
# ℹ 1 more variable: ess_tail <num>
We have some basic HMC-based validity statistics we can check.
Show code
pnbd_cdnow_onehiermu1_stanfit$cmdstan_diagnose()File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu1-1.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu1-2.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu1-3.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu1-4.csv not found
No valid input files, exiting.
4.2 Visual Diagnostics of the Sample Validity
Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.
Show code
parameter_subset <- c(
"mu_mn",
"lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
"mu[1]", "mu[2]", "mu[3]", "mu[4]"
)
pnbd_cdnow_onehiermu1_stanfit$draws(inc_warmup = FALSE) |>
mcmc_trace(pars = parameter_subset) +
expand_limits(y = 0) +
labs(
x = "Iteration",
y = "Value",
title = "Traceplot of Sample of Lambda and Mu Values"
) +
theme(axis.text.x = element_text(size = 10))We also check \(N_{eff}\) as a quick diagnostic of the fit.
Show code
pnbd_cdnow_onehiermu1_stanfit |>
neff_ratio(pars = c("lambda", "mu")) |>
as.numeric() |>
mcmc_neff() +
ggtitle("Plot of Parameter Effective Sample Sizes")4.3 Assess the Model
As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.
Show code
pnbd_stanfit <- pnbd_cdnow_onehiermu1_stanfit |>
recover_types(customer_fit_stats_tbl)
pnbd_cdnow_onehiermu1_assess_data_lst <- run_model_assessment(
model_stanfit = pnbd_stanfit,
insample_tbl = customer_fit_subset_tbl,
fit_label = "pnbd_cdnow_onehiermu1",
fit_end_dttm = use_fit_end_date |> as.POSIXct(),
valid_start_dttm = use_valid_start_date |> as.POSIXct(),
valid_end_dttm = use_valid_end_date |> as.POSIXct(),
sim_seed = 4210
)
pnbd_cdnow_onehiermu1_assess_data_lst |> glimpse()List of 5
$ model_fit_index_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu1_assess_fit_index_tbl.rds"
$ model_valid_index_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu1_assess_valid_index_tbl.rds"
$ model_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu1_assess_model_simstats_tbl.rds"
$ model_fit_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu1_assess_fit_simstats_tbl.rds"
$ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_onehiermu1_assess_valid_simstats_tbl.rds"
4.3.1 Check In-Sample Data Validation
We first check the model against the in-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehiermu1_assess_data_lst |>
use_series(model_fit_simstats_filepath) |>
read_rds()
insample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = customer_fit_subset_tbl,
simdata_tbl = simdata_tbl
)
insample_plots_lst$multi_plot |> print()Show code
insample_plots_lst$total_plot |> print()Show code
insample_plots_lst$quant_plot |> print()This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.
4.3.2 Check Out-of-Sample Data Validation
We now repeat for the out-of-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehierlambda1_assess_data_lst |>
use_series(model_valid_simstats_filepath) |>
read_rds()
outsample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = customer_valid_subset_tbl,
simdata_tbl = simdata_tbl
)
outsample_plots_lst$multi_plot |> print()Show code
outsample_plots_lst$total_plot |> print()Show code
outsample_plots_lst$quant_plot |> print()As for our short time frame data, overall our model is working well.
5 Fit Second Hierarchical Mu Model
In this model, we are going with a broadly similar model but we are instead using a different mean for our hierarchical prior.
5.1 Fit Stan Model
We now want to fit the model to our data using this alternative prior for lambda_mn.
Show code
stan_modelname <- "pnbd_cdnow_onehiermu2"
stanfit_prefix <- str_c("fit_", stan_modelname)
stanfit_seed <- stanfit_seed + 1
stanfit_object_file <- glue("data/{stanfit_prefix}_stanfit.rds")
stan_data_lst <- customer_fit_stats_tbl |>
select(customer_id, x, t_x, T_cal) |>
compose_data(
hier_mu_mn_p1 = 0.25,
hier_mu_mn_p2 = 1.00,
lambda_mn = 0.25,
lambda_cv = 1.00,
mu_cv = 1.00
)
if(!file_exists(stanfit_object_file)) {
pnbd_cdnow_onehiermu2_stanfit <- pnbd_onehiermu_stanmodel$sample(
data = stan_data_lst,
chains = 4,
iter_warmup = 500,
iter_sampling = 500,
seed = stanfit_seed,
save_warmup = TRUE,
output_dir = stan_modeldir,
output_basename = stanfit_prefix,
)
pnbd_cdnow_onehiermu2_stanfit$save_object(stanfit_object_file, compress = "gzip")
} else {
pnbd_cdnow_onehiermu2_stanfit <- read_rds(stanfit_object_file)
}
pnbd_cdnow_onehiermu2_stanfit$summary()# A tibble: 70,713 × 10
variable mean median sd mad q5 q95 rhat ess_bulk
<chr> <num> <num> <num> <num> <num> <num> <num> <num>
1 lp__ -2.33e+5 -2.33e+5 1.64e+2 1.65e+2 -2.33e+5 -2.32e+5 1.00 626.
2 mu_mn 1.15e-1 1.15e-1 1.85e-3 1.83e-3 1.12e-1 1.18e-1 1.00 617.
3 lambda[1] 1.42e-1 8.26e-2 1.68e-1 9.33e-2 6.04e-3 4.78e-1 1.00 2327.
4 lambda[2] 3.41e-1 2.76e-1 2.67e-1 2.18e-1 5.08e-2 8.84e-1 1.00 3455.
5 lambda[3] 9.10e-2 8.47e-2 4.01e-2 3.83e-2 3.76e-2 1.65e-1 1.00 3634.
6 lambda[4] 7.28e-2 6.67e-2 3.84e-2 3.50e-2 2.25e-2 1.44e-1 1.00 4492.
7 lambda[5] 1.81e-1 1.75e-1 5.66e-2 5.70e-2 9.88e-2 2.83e-1 1.00 4414.
8 lambda[6] 1.46e-1 8.56e-2 1.74e-1 9.97e-2 4.41e-3 4.88e-1 1.00 2718.
9 lambda[7] 3.73e-2 3.14e-2 2.73e-2 2.31e-2 6.04e-3 8.92e-2 1.00 4041.
10 lambda[8] 1.25e-1 1.19e-1 4.99e-2 5.03e-2 5.63e-2 2.15e-1 1.00 2988.
# ℹ 70,703 more rows
# ℹ 1 more variable: ess_tail <num>
We have some basic HMC-based validity statistics we can check.
Show code
pnbd_cdnow_onehiermu2_stanfit$cmdstan_diagnose()File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu2-1.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu2-2.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu2-3.csv not found
File /home/rstudio/btydwork/stan_models/fit_pnbd_cdnow_onehiermu2-4.csv not found
No valid input files, exiting.
5.2 Visual Diagnostics of the Sample Validity
Now that we have a sample from the posterior distribution we need to create a few different visualisations of the diagnostics.
Show code
parameter_subset <- c(
"mu_mn",
"lambda[1]", "lambda[2]", "lambda[3]", "lambda[4]",
"mu[1]", "mu[2]", "mu[3]", "mu[4]"
)
pnbd_cdnow_onehiermu2_stanfit$draws(inc_warmup = FALSE) |>
mcmc_trace(pars = parameter_subset) +
expand_limits(y = 0) +
labs(
x = "Iteration",
y = "Value",
title = "Traceplot of Sample of Lambda and Mu Values"
) +
theme(axis.text.x = element_text(size = 10))We also check \(N_{eff}\) as a quick diagnostic of the fit.
Show code
pnbd_cdnow_onehiermu2_stanfit |>
neff_ratio(pars = c("lambda", "mu")) |>
as.numeric() |>
mcmc_neff() +
ggtitle("Plot of Parameter Effective Sample Sizes")5.3 Assess the Model
As we intend to run the same logic to assess each of our models, we have combined all this logic into a single function run_model_assessment, to run the simulations and combine the datasets.
Show code
pnbd_stanfit <- pnbd_cdnow_onehiermu2_stanfit |>
recover_types(customer_fit_stats_tbl)
pnbd_cdnow_onehiermu2_assess_data_lst <- run_model_assessment(
model_stanfit = pnbd_stanfit,
insample_tbl = customer_fit_subset_tbl,
fit_label = "pnbd_cdnow_onehiermu2",
fit_end_dttm = use_fit_end_date |> as.POSIXct(),
valid_start_dttm = use_valid_start_date |> as.POSIXct(),
valid_end_dttm = use_valid_end_date |> as.POSIXct(),
sim_seed = 4210
)
pnbd_cdnow_onehiermu2_assess_data_lst |> glimpse()List of 5
$ model_fit_index_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu2_assess_fit_index_tbl.rds"
$ model_valid_index_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu2_assess_valid_index_tbl.rds"
$ model_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu2_assess_model_simstats_tbl.rds"
$ model_fit_simstats_filepath : 'glue' chr "data/pnbd_cdnow_onehiermu2_assess_fit_simstats_tbl.rds"
$ model_valid_simstats_filepath: 'glue' chr "data/pnbd_cdnow_onehiermu2_assess_valid_simstats_tbl.rds"
5.3.1 Check In-Sample Data Validation
We first check the model against the in-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehiermu2_assess_data_lst |>
use_series(model_fit_simstats_filepath) |>
read_rds()
insample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = customer_fit_subset_tbl,
simdata_tbl = simdata_tbl
)
insample_plots_lst$multi_plot |> print()Show code
insample_plots_lst$total_plot |> print()Show code
insample_plots_lst$quant_plot |> print()This fit looks reasonable and appears to capture most of the aspects of the data used to fit it. Given that this is a synthetic dataset, this is not surprising, but at least we appreciate that our model is valid.
5.3.2 Check Out-of-Sample Data Validation
We now repeat for the out-of-sample data.
Show code
simdata_tbl <- pnbd_cdnow_onehiermu1_assess_data_lst |>
use_series(model_valid_simstats_filepath) |>
read_rds()
outsample_plots_lst <- create_model_assessment_plots(
obsdata_tbl = customer_valid_subset_tbl,
simdata_tbl = simdata_tbl
)
outsample_plots_lst$multi_plot |> print()Show code
outsample_plots_lst$total_plot |> print()Show code
outsample_plots_lst$quant_plot |> print()As for our short time frame data, overall our model is working well.
6 Compare Model Outputs
We have looked at each of the models individually, but it is also worth looking at each of the models as a group.
Show code
calculate_simulation_statistics <- function(file_rds) {
simdata_tbl <- read_rds(file_rds)
multicount_cust_tbl <- simdata_tbl |>
filter(sim_tnx_count > 0) |>
count(draw_id, name = "multicust_count")
totaltnx_data_tbl <- simdata_tbl |>
count(draw_id, wt = sim_tnx_count, name = "simtnx_count")
simstats_tbl <- multicount_cust_tbl |>
inner_join(totaltnx_data_tbl, by = "draw_id")
return(simstats_tbl)
}Show code
obs_fit_customer_count <- customer_fit_subset_tbl |>
filter(tnx_count > 0) |>
nrow()
obs_valid_customer_count <- customer_valid_subset_tbl |>
filter(tnx_count > 0) |>
nrow()
obs_fit_total_count <- customer_fit_subset_tbl |>
pull(tnx_count) |>
sum()
obs_valid_total_count <- customer_valid_subset_tbl |>
pull(tnx_count) |>
sum()
obs_stats_tbl <- tribble(
~assess_type, ~name, ~obs_value,
"fit", "multicust_count", obs_fit_customer_count,
"fit", "simtnx_count", obs_fit_total_count,
"valid", "multicust_count", obs_valid_customer_count,
"valid", "simtnx_count", obs_valid_total_count
)
model_assess_tbl <- dir_ls("data", regexp = "pnbd_cdnow_(one|fixed).*_assess_.*simstats") |>
enframe(name = NULL, value = "file_path") |>
filter(str_detect(file_path, "_assess_model_", negate = TRUE)) |>
mutate(
model_label = str_replace(file_path, "data/pnbd_cdnow_(.*?)_assess_.*", "\\1"),
assess_type = if_else(str_detect(file_path, "_assess_fit_"), "fit", "valid"),
sim_data = map(
file_path, calculate_simulation_statistics,
.progress = "calculate_simulation_statistics"
)
)
model_assess_tbl |> glimpse()Rows: 16
Columns: 4
$ file_path <fs::path> "data/pnbd_cdnow_fixed1_assess_fit_simstats_tbl.rds",…
$ model_label <chr> "fixed1", "fixed1", "fixed2", "fixed2", "fixed3", "fixed3"…
$ assess_type <chr> "fit", "valid", "fit", "valid", "fit", "valid", "fit", "va…
$ sim_data <list> [<tbl_df[2000 x 3]>], [<tbl_df[2000 x 3]>], [<tbl_df[2000…
Show code
model_assess_summstat_tbl <- model_assess_tbl |>
select(model_label, assess_type, sim_data) |>
unnest(sim_data) |>
pivot_longer(
cols = !c(model_label, assess_type, draw_id)
) |>
group_by(model_label, assess_type, name) |>
summarise(
.groups = "drop",
mean_val = mean(value),
p10 = quantile(value, 0.10),
p25 = quantile(value, 0.25),
p50 = quantile(value, 0.50),
p75 = quantile(value, 0.75),
p90 = quantile(value, 0.90)
)
model_assess_summstat_tbl |> glimpse()Rows: 32
Columns: 9
$ model_label <chr> "fixed1", "fixed1", "fixed1", "fixed1", "fixed2", "fixed2"…
$ assess_type <chr> "fit", "fit", "valid", "valid", "fit", "fit", "valid", "va…
$ name <chr> "multicust_count", "simtnx_count", "multicust_count", "sim…
$ mean_val <dbl> 1098.7000, 4283.9665, 297.7140, 914.8950, 1299.9255, 4667.…
$ p10 <dbl> 1072.0, 4090.0, 283.0, 854.0, 1272.0, 4484.9, 181.0, 548.0…
$ p25 <dbl> 1084.00, 4181.00, 290.00, 882.00, 1285.75, 4570.00, 187.00…
$ p50 <dbl> 1099.0, 4277.0, 297.0, 915.0, 1300.0, 4663.0, 194.0, 605.0…
$ p75 <dbl> 1114.00, 4384.25, 306.00, 948.00, 1314.00, 4765.00, 201.00…
$ p90 <dbl> 1126.0, 4479.0, 313.0, 979.0, 1328.0, 4850.0, 207.0, 662.0…
Show code
#! echo: TRUE
ggplot(model_assess_summstat_tbl) +
geom_errorbar(
aes(x = model_label, ymin = p10, ymax = p90), width = 0
) +
geom_errorbar(
aes(x = model_label, ymin = p25, ymax = p75), width = 0, linewidth = 3
) +
geom_hline(
aes(yintercept = obs_value),
data = obs_stats_tbl, colour = "red"
) +
scale_y_continuous(labels = label_comma()) +
expand_limits(y = 0) +
facet_wrap(
vars(assess_type, name), scale = "free_y"
) +
labs(
x = "Model",
y = "Count",
title = "Comparison Plot for the Different Models"
) +
theme(
axis.text.x = element_text(angle = 20, vjust = 0.5, size = 8)
)6.1 Write Assessment Data to Disk
We now want to save the assessment data to disk.
Show code
model_assess_tbl |> write_rds("data/assess_data_pnbd_cdnow_onehier_tbl.rds")7 R Environment
Show code
options(width = 120L)
sessioninfo::session_info()─ Session info ───────────────────────────────────────────────────────────────────────────────────────────────────────
setting value
version R version 4.2.3 (2023-03-15)
os Ubuntu 22.04.2 LTS
system x86_64, linux-gnu
ui X11
language (EN)
collate en_US.UTF-8
ctype en_US.UTF-8
tz Europe/Dublin
date 2023-08-22
pandoc 2.19.2 @ /usr/local/bin/ (via rmarkdown)
─ Packages ───────────────────────────────────────────────────────────────────────────────────────────────────────────
package * version date (UTC) lib source
abind 1.4-5 2016-07-21 [1] RSPM (R 4.2.0)
arrayhelpers 1.1-0 2020-02-04 [1] RSPM (R 4.2.0)
backports 1.4.1 2021-12-13 [1] RSPM (R 4.2.0)
base64enc 0.1-3 2015-07-28 [1] RSPM (R 4.2.0)
bayesplot * 1.10.0 2022-11-16 [1] RSPM (R 4.2.0)
bit 4.0.5 2022-11-15 [1] RSPM (R 4.2.0)
bit64 4.0.5 2020-08-30 [1] RSPM (R 4.2.0)
boot 1.3-28.1 2022-11-22 [2] CRAN (R 4.2.3)
bridgesampling 1.1-2 2021-04-16 [1] RSPM (R 4.2.0)
brms * 2.19.0 2023-03-14 [1] RSPM (R 4.2.0)
Brobdingnag 1.2-9 2022-10-19 [1] RSPM (R 4.2.0)
cachem 1.0.7 2023-02-24 [1] RSPM (R 4.2.0)
callr 3.7.3 2022-11-02 [1] RSPM (R 4.2.0)
checkmate 2.1.0 2022-04-21 [1] RSPM (R 4.2.0)
cli 3.6.1 2023-03-23 [1] RSPM (R 4.2.0)
cmdstanr * 0.5.3 2023-07-21 [1] Github (stan-dev/cmdstanr@22b391e)
coda 0.19-4 2020-09-30 [1] RSPM (R 4.2.0)
codetools 0.2-19 2023-02-01 [2] CRAN (R 4.2.3)
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colourpicker 1.2.0 2022-10-28 [1] RSPM (R 4.2.0)
conflicted * 1.2.0 2023-02-01 [1] RSPM (R 4.2.0)
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crayon 1.5.2 2022-09-29 [1] RSPM (R 4.2.0)
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digest 0.6.31 2022-12-11 [1] RSPM (R 4.2.0)
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pillar 1.9.0 2023-03-22 [1] RSPM (R 4.2.0)
pkgbuild 1.4.0 2022-11-27 [1] RSPM (R 4.2.0)
pkgconfig 2.0.3 2019-09-22 [1] RSPM (R 4.2.0)
plyr 1.8.8 2022-11-11 [1] RSPM (R 4.2.0)
posterior * 1.4.1 2023-03-14 [1] RSPM (R 4.2.0)
prettyunits 1.1.1 2020-01-24 [1] RSPM (R 4.2.0)
processx 3.8.1 2023-04-18 [1] RSPM (R 4.2.0)
projpred 2.5.0 2023-04-05 [1] RSPM (R 4.2.0)
promises 1.2.0.1 2021-02-11 [1] RSPM (R 4.2.0)
ps 1.7.5 2023-04-18 [1] RSPM (R 4.2.0)
purrr * 1.0.1 2023-01-10 [1] RSPM (R 4.2.0)
quadprog 1.5-8 2019-11-20 [1] RSPM (R 4.2.0)
R6 2.5.1 2021-08-19 [1] RSPM (R 4.2.0)
Rcpp * 1.0.10 2023-01-22 [1] RSPM (R 4.2.0)
RcppParallel 5.1.7 2023-02-27 [1] RSPM (R 4.2.0)
readr * 2.1.4 2023-02-10 [1] RSPM (R 4.2.0)
reshape2 1.4.4 2020-04-09 [1] RSPM (R 4.2.0)
rlang * 1.1.0 2023-03-14 [1] RSPM (R 4.2.0)
rmarkdown 2.21 2023-03-26 [1] RSPM (R 4.2.0)
rstan 2.21.8 2023-01-17 [1] RSPM (R 4.2.0)
rstantools 2.3.1 2023-03-30 [1] RSPM (R 4.2.0)
rsyslog * 1.0.2 2021-06-04 [1] RSPM (R 4.2.0)
scales * 1.2.1 2022-08-20 [1] RSPM (R 4.2.0)
sessioninfo 1.2.2 2021-12-06 [1] RSPM (R 4.2.0)
shiny 1.7.4 2022-12-15 [1] RSPM (R 4.2.0)
shinyjs 2.1.0 2021-12-23 [1] RSPM (R 4.2.0)
shinystan 2.6.0 2022-03-03 [1] RSPM (R 4.2.0)
shinythemes 1.2.0 2021-01-25 [1] RSPM (R 4.2.0)
StanHeaders 2.21.0-7 2020-12-17 [1] RSPM (R 4.2.0)
stringi 1.7.12 2023-01-11 [1] RSPM (R 4.2.0)
stringr * 1.5.0 2022-12-02 [1] RSPM (R 4.2.0)
svUnit 1.0.6 2021-04-19 [1] RSPM (R 4.2.0)
tensorA 0.36.2 2020-11-19 [1] RSPM (R 4.2.0)
threejs 0.3.3 2020-01-21 [1] RSPM (R 4.2.0)
tibble * 3.2.1 2023-03-20 [1] RSPM (R 4.2.0)
tidybayes * 3.0.4 2023-03-14 [1] RSPM (R 4.2.0)
tidyr * 1.3.0 2023-01-24 [1] RSPM (R 4.2.0)
tidyselect 1.2.0 2022-10-10 [1] RSPM (R 4.2.0)
tidyverse * 2.0.0 2023-02-22 [1] RSPM (R 4.2.0)
timechange 0.2.0 2023-01-11 [1] RSPM (R 4.2.0)
tzdb 0.3.0 2022-03-28 [1] RSPM (R 4.2.0)
utf8 1.2.3 2023-01-31 [1] RSPM (R 4.2.0)
vctrs 0.6.2 2023-04-19 [1] RSPM (R 4.2.0)
vroom 1.6.1 2023-01-22 [1] RSPM (R 4.2.0)
withr 2.5.0 2022-03-03 [1] RSPM (R 4.2.0)
xfun 0.38 2023-03-24 [1] RSPM (R 4.2.0)
xtable 1.8-4 2019-04-21 [1] RSPM (R 4.2.0)
xts 0.13.1 2023-04-16 [1] RSPM (R 4.2.0)
yaml 2.3.7 2023-01-23 [1] RSPM (R 4.2.0)
zoo 1.8-12 2023-04-13 [1] RSPM (R 4.2.0)
[1] /usr/local/lib/R/site-library
[2] /usr/local/lib/R/library
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